As part of their chores on Saturday mornings, they have to clean the bathrooms and wash the floors of the house while their parents go grocery shopping. In one hour’s time, Mike can clean two bathrooms or wash six floors. Linda, on the other hand, can clean three bathrooms or wash seven floors. The house has four bathrooms and ten rooms’ worth of floors. All along, Mike and Linda have been splitting up the work in half for each job, and thus every Saturday, each has been cleaning two bathrooms and five floors respectively.
1.Who has an absolute advantage in cleaning the most bathrooms and floors in the least amount of time?
2.On the basis of comparative advantage, who has a comparative advantage in cleaning bathrooms in the least amount of time, and who has a comparative advantage in cleaning floors in the least amount of time?
3.If Mike and Linda wish to reduce their opportunity costs of spending time cleaning on Saturdays, how much time will each save each Saturday if specialization based upon comparative advantages is used to divide up the work?
1) Linda
2) Mike then Linda
3)?
1. To determine who has an absolute advantage in cleaning the most bathrooms and floors in the least amount of time, we need to compare the cleaning rates of Mike and Linda.
From the given information, we know that Mike can clean 2 bathrooms in 1 hour, while Linda can clean 3 bathrooms in 1 hour. Additionally, Mike can wash 6 floors in 1 hour, while Linda can wash 7 floors in 1 hour.
Therefore, Linda has an absolute advantage in cleaning both bathrooms and floors in the least amount of time because she can clean more bathrooms and wash more floors in the same time frame as Mike.
2. Comparative advantage is based on the opportunity cost of producing a particular good or service. To determine who has a comparative advantage in cleaning bathrooms and floors, we need to compare their cleaning rates and calculate the opportunity costs.
For cleaning bathrooms, we compare Mike's and Linda's rates:
- Mike can clean 2 bathrooms in 1 hour, so his opportunity cost of cleaning a bathroom is 0.5 floors (1 hour / 2 bathrooms = 0.5 hour/bathroom).
- Linda can clean 3 bathrooms in 1 hour, so her opportunity cost of cleaning a bathroom is approximately 0.33 floors (1 hour / 3 bathrooms = 0.33 hour/bathroom).
Comparing the opportunity costs, Linda has a lower opportunity cost of cleaning bathrooms (0.33 floors/bathroom) compared to Mike (0.5 floors/bathroom). Therefore, Linda has a comparative advantage in cleaning bathrooms in the least amount of time.
For cleaning floors, we compare Mike's and Linda's rates:
- Mike can wash 6 floors in 1 hour, so his opportunity cost of washing a floor is 0.17 bathrooms (1 hour / 6 floors = 0.17 hour/floor).
- Linda can wash 7 floors in 1 hour, so her opportunity cost of washing a floor is approximately 0.14 bathrooms (1 hour / 7 floors = 0.14 hour/floor).
Comparing the opportunity costs, Linda has a lower opportunity cost of cleaning floors (0.14 bathrooms/floor) compared to Mike (0.17 bathrooms/floor). Therefore, Linda has a comparative advantage in cleaning floors in the least amount of time.
3. To reduce their opportunity costs of spending time cleaning on Saturdays, Mike and Linda should specialize in the task where they have a comparative advantage.
Since Linda has a comparative advantage in cleaning bathrooms, she should focus on cleaning all the bathrooms. If there are 4 bathrooms in the house, she can clean all of them in 4/3 hours (1 hour for 3 bathrooms), saving 2/3 of an hour.
Similarly, since Linda has a comparative advantage in cleaning floors, she should focus on washing all the floors. If there are 10 rooms' worth of floors, she can wash them in approximately 1.43 hours (1 hour for 7 floors), saving around 0.57 of an hour.
On the other hand, Mike can take up other tasks or divide his time between assisting Linda and doing other activities.